A fast algorithm for computing Bell polynomials based on index\n break-downs using prime factorization

2020/04/17 by Hamed Taghavian, Taghavian, Hamed · 2 citations
Computer Science · Engineering · #Polynomial and algebraic computation #Optical Network Technologies

paper · pdf · doi:10.48550/arxiv.2004.09283

Abstract

By establishing an interesting connection between ordinary Bell polynomials\nand rational convolution powers, some composition and inverse relations of Bell\npolynomials as well as explicit expressions for convolution roots of sequences\nare obtained. Based on these results, a new method is proposed for calculation\nof partial Bell polynomials based on prime factorization. It is shown that this\nmethod is more efficient than the conventional recurrence procedure for\ncomputing Bell polynomials in most cases, requiring far less arithmetic\noperations. A detailed analysis of the computation complexity is provided,\nfollowed by some numerical evaluations.\n

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• Point-to-ellipse Fourier series
• Some nonlinear inverse relations of Bell polynomials via the Lagrange inversion formula

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